We consider n-linear Nambu brackets in dimension N higher than n. Starting from a Hamiltonian system with Poisson bracket and K Casimir invariants defined the phase space of = + 2M, where M is number effective degrees freedom, we investigate necessary sufficient condition for this to possess brackets. For case n 3, by looking possible solutions fundamental identity, found be 2, i.e., should hav...

Abstract We prove a product formula for the determinant of cohomology an étale sheaf with $\ell $ -adic coefficients over arbitrary proper scheme perfect field positive characteristic p distinct from . The local contributions are constructed by iterating vanishing cycle functors as well certain exact additive that can be considered linearised versions Artin conductors and $\varepsilon -factors....